Acquisition mechanism for a mobile satellite system

ABSTRACT

A method for enabling synchronization of a communications terminal in a wireless communication system, and a corresponding acquisition system of the communications terminal, wherein the method consists of the steps of: receiving a burst at a receiver of the communications terminal, the burst containing a composite waveform including two or more component waveforms, wherein each of the two or more waveforms has a known frequency variation throughout the burst; detecting the presence of the composite waveform; and estimating a frequency offset and a timing offset of the composite waveform as received into the receiver, whereby synchronization is achieved.

This application claims priority under 35 U.S.C § 119(e) to U.S.Provisional Patent Application Ser. No. 60/109,671, filed Nov. 24, 1998,of Vishwanath et al., for ACQUISITION MECHANISM FOR A MOBILE SATELLITESYSTEM, which U.S. Provisional Patent Application is incorporated hereinby reference.

This application is related to U.S. Patent Application Ser. No.09/447,685, filed concurrently herewith Nov. 23, 1999, of Vishwanath etal., for WAVEFORM SUPPORTING SYNCHRONIZATION IN MOBILE SATELLITESYSTEMS; now U.S. Pat. No. 6,418,158, which is incorporated herein byreference.

BACKGROUND OF THE INVENTION

The present invention relates to signal synchronization, and moreparticularly to signal synchronization in a communications system. Evenmore particularly, the present invention relates to synchronization ofwireless transceivers by transmitting a composite waveform having aknown frequency variation to an unsynchronized wireless transceiver of amobile satellite communications system for signal synchronization and acorresponding method of acquiring the composite waveform at theunsynchronized transceiver.

In mobile communications systems, such as a mobile satellitecommunications system, mobile communications terminals (i.e. mobileterminals or transceivers) are frequently placed in positions in whichthey cannot maintain synchronization with a satellite. For example, themobile terminal might be turned off and stored, may be carried into abuilding with significant signal attenuation, or may be newly purchased.In any case, the mobile terminal must be able to find the signals sentfrom a satellite for synchronization prior to being able to begincommunication. As is typically the case, a terrestrial gateway stationor base station is constantly transmitting bursts containing waveformsused for synchronization over a specified channel, such as a frequencycontrol channel (hereinafter referred to as FCCH). The mobile terminalmust find the signal waveform that is transmitted from the gatewaystation via the satellite in order to be able to begin communicationwith the gateway station via the satellite. This process is commonlyreferred to as acquisition.

The gateway station will transmit a synchronization waveform (alsoreferred to as a waveform or signal waveform) as a limited durationburst, e.g. 5 msec, periodically, e.g. once every 320 msec. In acquiringthe synchronization signal, a mobile terminal will typically have tosearch within about one thousand communications channels (i.e. channels)of a communications link to find the waveform over the period of 320msec for the 5 msec waveform. Often, to save processing duringacquisition at the mobile terminal, the mobile terminal will look atapproximately ten preassigned channels of the one thousand channels forthe transmitted waveform. The mobile terminal must search in differentchannels because the burst containing the waveform does not usuallyarrive at the same frequency that the waveform is transmitted at due tofrequency shifts/offsets from the gateway station to the satellite andfrom the satellite to the mobile terminal. Furthermore, the mobileterminal does not know at what time within any given 320 msec window the5 msec waveform will arrive.

In the prior art, such waveforms are detectable at the mobile terminals.A requirement of such waveforms is that a signal frequency (or carrierfrequency) of the waveform be known. However, because of signaldegradation and distortions due to all forms of time delays, propagationdelays, doppler shifting, and noise, it is necessary to compensate forthe frequency and/or time shifting of the waveform.

By way of background, time delays result from several factors. Timedelays may be caused by obstructions in a dominant signal path thatgenerate “multi-paths” to occur from scattered paths resulting fromreflections off the obstructions. The differences in distance betweenthe multi-paths result in timing offsets as well as fading of thesignal, depending upon the type of channel (e.g. Rician or Rayleighfading). Also, in mobile satellite communications systems, inparticular, relative motion between the satellite and the mobileterminal due to a velocity of the satellite as it orbits the Earth andanother velocity of the terminal as it is operated from a movingvehicle, for example, results in varying time delay by the signalstraveling between the satellite and the mobile terminal. Even astationary mobile terminal may experience relative motion between itselfand the satellite due to motion of the satellite in orbit. For example,in a geostationary satellite system, the satellite follows anapproximately sinusoidal pattern of north-south movement in orbit. Assuch, if the satellite and the mobile terminal are moving towards eachother, a transmitted signal from the satellite will arrive earlier andearlier as the relative movement continues.

Doppler shifting is also the result of such relative movement of thesatellite and the mobile terminal. As the mobile terminal and thesatellite move toward one another, frequencies appear to get higher, butas the mobile terminal and the satellite move away from one another,frequencies appear to get lower.

This gives rise to a need for a new type of signal waveform used forsynchronization that can easily be detected and be resolved for dopplershifting (i.e. frequency offsets) and time delays.

Furthermore, in the prior art, different types of signal waveforms aretransmitted from the gateway station to a mobile terminals viasatellites for synchronization. This is because in satellitecommunications systems, many different services are provided thatoperate at disparate bandwidths and tolerate disparate levels of signalattenuation and minimum signal-to-noise ratios (SNRs). Consequently,current mobile satellite systems require more than one type of waveformto be used for the many different services.

As an example, one key service provided by the mobile satellite systemsis voice or data communication. Effective voice communication requiresthat channel attenuations be less than an order of 10 dB whereas otherservices, such as alerting, may only require that channel attenuationsbe less than an order of 30 dB. By way of example, if a tree wereblocking the line-of-sight path of a voice signal between a satelliteand the terminal, and attenuated a voice signal from the satellite byless than 10 dB, the voice signal could still be received by the mobileterminal. However, if a building were blocking the line-of-sight path ofthe voice signal and attenuated the voice signal by 20 dB, then themobile terminal could not receive the voice signal but could still trackand receive an alerting signal from the satellite.

In contrast, in “alerting”, the mobile satellite system typicallytolerates very low signal conditions as compared with conditions thatcan be tolerated by a typical voice signal. Specifically, there istypically a 20 dB difference in channel attenuation levels betweenconditions in which an alert signal can be successfully received andconditions in which a voice signal can be successfully received. Thus,conditions supporting alert signals will not necessarily support voicesignals in the same mobile satellite system.

Thus, in order to accommodate the use of such varying signal leveltolerances (e.g. voice services and alerting services) the prior artutilizes distinct waveforms for each distinct service, e.g., onewaveform for tracking alerting, and another waveform for synchronizingvoice communications.

Thus, there is a need in the wireless communication industry to providea waveform that supports a variety of services under different signalconditions to conserve power and resources in the mobile satellitesystem.

One example of a prior art waveform which is easily detectable andresolvable for frequency shifting, but not timing offsets, and which hasbeen used in prior art communications systems is a sinusoidal waveform,or a “tone”, which has a constant frequency over time. An example ofsuch a tone is a sine wave or cosine wave with any random phase φ.

Although sinusoidal waveforms or tones are easily detectable by mobileterminals, they present a problem of “spurs” in the received frequencywhen the tone travels in mobile terminal's hardware. The receiverhardware of the mobile terminal typically sees a received waveform (i.e.tone) as a very low level signal. Furthermore, a receiver typicallyincludes a variety of frequency sources that tend to induce sinusoids tothe received signal (i.e. tone), making distinctions between thereceived signal and the induced sinusoids difficult to discern.

These induced sinusoids are called “spurs” which are essentiallyfrequency-domain spikes. When spurs occur in the receiver, there can bea loss of synchronization because the waveform of interest (i.e. thetone) may be lost. One way to avoid these spurs is to change RF hardwareso that they are eliminated by the hardware, however this is costly andtakes space and power within the hardware itself.

Thus, another desirable design constraint of the waveform (which may bereferred to as a synchronization signal) is that it not require acomplex receiver or complicated changes to standard receiver hardwareand that the waveform not induce hardware related degradation thereof.In particular, the waveform must be robust against induced spurs.

Other prior art methods have eliminated the problem of “spurs” byimplicitly spreading the spurs by using a signal waveform such as aQuadrature Phase Shift Keyed (QPSK) signal. Such a QPSK signal ismodulated according to phase and therefore is not correlated to thespurs. Although the QPSK modulated signal solves the problem of spurs,it does not solve the detectability of varying signal levels used inmultiple levels of services, such as voice and alerting services.

Other prior art methods have used, as the waveform used forsynchronization, a tone followed by a modulated waveform, wherein thetone is used to compute frequency and the modulated waveform is used tocompute timing. Although the use of the tone followed by the modulatedwaveform solves the problem caused by induced spurs, it exhausts systemresources such as power, bandwidth and time, and is not well-suited totwo or more levels of service, such as alerting and voice communication.

With regard to the acquisition of the waveform at a mobile terminal, andconsidering several of the above stated concerns it is desirable totransmit a waveform that is easily detectable, can resolve bothfrequency and timing offsets, avoids the problem of “spurs” in thereceiver, and can support different types of services, e.g. acquisitionof voice services and tracking of alerting. Thus, such a waveform shouldbe practical to implement on a digital signal processor, for example,using a Fast Fourier Transform (FFT), should not resemble a tone, andshould not require hardware modifications in the receiver.

The present invention advantageously addresses the above and otherneeds.

SUMMARY OF THE INVENTION

The present invention advantageously addresses the needs above as wellas other needs by providing a method and apparatus for the acquisitionof received waveforms that are used for the synchronization of wirelesscommunications terminals, and the estimation of the frequency offset andtiming offset of the received waveforms.

In one embodiment, the present invention can be characterized as amethod for enabling synchronization of a communications terminal in awireless communication system comprising the step of receiving a burstat a receiver of the communications terminal, the burst containing acomposite waveform including two or more component waveforms, whereineach of the two or more waveforms has a known frequency variationthroughout the burst. The composite waveform has a composite bandwidthon an order of an available channel bandwidth, and wherein each of saidtwo or more component waveforms has a component bandwidth on the orderof the available channel bandwidth. Additionally, a range of values forthe differences between the instantaneous frequencies of two of said twoor more component waveforms is on an order of twice of said availablechannel bandwidth.

In another embodiment, the present invention may be characterized as anacquisition system of a wireless communications terminal for acquiring areceived composite waveform including two or more component waveformsand estimating a frequency offset and a timing offset of the receivedcomposite waveform. The acquisition system includes a first phaseshifter for desweeping a first component waveform of the receivedcomposite waveform and a first processor coupled to the first phaseshifter for transforming the first component waveform having beendeswept into a first frequency domain representation. Furthermore, theacquisition system includes a second phase shifter for desweeping asecond component waveform of said received composite waveform and asecond processor coupled to the second phase shifter for transformingthe second component waveform, having been deswept, into a secondfrequency domain representation. Furthermore, a detection processor iscoupled to said first processor for detecting a peak of said firstfrequency domain representation, thus, detecting the presence of saidfirst component waveform. The detection processor includes a parameterestimator for computing said frequency offset and said timing offset ofsaid received composite waveform, having been detected.

In a further embodiment, the present invention may be characterized as amethod for enabling synchronization of a communications terminal in awireless communication system comprising the steps of: receiving a burstat a receiver of the communications terminal, the burst containing acomposite waveform including two or more component waveforms, whereineach of the two or more waveforms has a known frequency variationthroughout the burst; detecting the presence of the composite waveform;and estimating a frequency offset and a timing offset of the compositewaveform as received into said receiver, whereby synchronization isachieved.

In a preferred embodiment, the composite waveform may be a dual-chirpwaveform including an up-chirp component waveform and a down-chirpcomponent waveform.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features and advantages of the presentinvention will be more apparent from the following more particulardescription thereof, presented in conjunction with the followingdrawings wherein:

FIG. 1 is a block diagram of a satellite communications system in whichthe present invention may be employed in accordance herewith;

FIG. 2 is a block diagram illustrating contributions to a waveform asthe waveform is transmitted from a source transmitter, e.g. a gatewaystation, during propagation along a line-of-sight path to a receiver,e.g. via a satellite;

FIG. 3 is a plot of amplitude versus time for the composite waveform(also referred to as a composite signal waveform) in accordance with oneembodiment of the present invention, shown as a dual-chirp waveform thatincludes an up-chirp waveform and a down-chirp waveform, which may betransmitted by the gateway station 24 to the mobile terminal 12 of thesatellite communication system of FIG. 1 prior to experiencing frequencyand timing offsets during transmission through the communications links;

FIG. 4 illustrates a plot of frequency versus time for the transmittedcomposite waveform, shown as the dual-chirp waveform including theup-chirp waveform and down-chirp waveform of the embodiment shown inFIG. 3, as would be transmitted in the satellite communication system ofFIG. 1;

FIG. 4A illustrates a plot of frequency versus time for a transmittedcomposite waveform not in accordance with the present invention, whichis shown as a comparison to the composite waveform of FIG. 4 and todistinguish the composite waveform of the present invention with othertypes of composite waveforms;

FIG. 5A illustrates a frequency versus time plot of the compositewaveform of FIGS. 3 and 4, shown as the dual-chirp waveform includingthe up-chirp waveform and the down-chirp waveform, that is transmittedfrom the gateway station 24 of the satellite communications system ofFIG. 1;

FIG. 5B illustrates a frequency versus time plot of the compositewaveform of FIG. 5A and the corresponding received composite waveform(dashed line) that is received at the mobile terminal 12 of FIG. 1,wherein a frequency offset has been introduced into the compositewaveform received;

FIG. 5C illustrates a frequency versus time plot of the compositewaveform of FIG. 5A and the corresponding received composite waveform(dashed line) that is received at the mobile terminal 12 of FIG. 1,wherein a timing offset has been introduced into the composite waveform;

FIG. 5D illustrates a frequency versus time plot of the compositewaveform of FIG. 5A and the corresponding received composite waveform(dashed line) that is received at the mobile terminal 12 of FIG. 1,wherein both a frequency offset and a timing offset have been introducedinto the composite waveform;

FIG. 6A illustrates a frequency versus time plot of the compositewaveform of FIG. 4A, shown as two down-chirp waveforms, that would notprovide accurate frequency and timing offset estimations at the mobileterminal, in contrast to the composite signal waveform as shown anddescribed in FIGS. 3 through 4 and 5A through 5D, wherein the average ofthe difference between the instantaneous frequencies of the twocomponent waveforms of the composite waveform over the duration of thecomposite waveform is not large;

FIG. 6B illustrates a frequency versus time plot of the compositewaveform of FIG. 6A and the corresponding received composite waveform(dashed line) that would be received at a mobile terminal, wherein afrequency offset has been introduced into the received compositewaveform;

FIG. 6C illustrates a frequency versus time plot of the compositewaveform of FIG. 6A and the corresponding received composite waveform(dashed line) that would be received at a mobile terminal, wherein atiming offset has been introduced into the received composite waveform;

FIG. 6D illustrates a frequency versus time plot of the compositewaveform of FIG. 6A and the corresponding received composite waveform(dashed line) that would be received at a mobile terminal, wherein botha frequency offset and a timing offset have been introduced into thecomposite waveform;

FIG. 7 is a block diagram of an Acquisition System found in the mobileterminal 12 of FIG. 1 that illustrates acquisition of the compositewaveform, which is shown as a dual-chirp waveform, such that adesweeping search algorithm is used for detection of the compositewaveform, which then enables synchronization of the mobile terminal tothe satellite communication system of FIG. 1;

FIG. 8 is an illustration of a sliding window process used by theacquisition system of FIG. 7 to scan for the composite signal waveform;

FIG. 9 is a flow chart of the steps performed for acquisition of thecomposite waveform, which is illustrated as the dual-chirp waveform ofFIGS. 3 and 4, which may be implemented by the acquisition system 100 ofFIG. 7 of the mobile terminal 12 of the satellite communications systemof FIG. 1;

FIG. 10 illustrates a plot of the amplitude of the Fourier TransformPeak over the course of the duration of the composite signal waveform,which is illustrated as the dual-chirp waveform.

Corresponding reference characters indicate corresponding componentsthroughout the several views of the drawings.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The following description of the presently contemplated best mode ofpracticing the invention is not to be taken in a limiting sense, but ismade merely for the purpose of describing the general principles of theinvention. The scope of the invention should be determined withreference to the claims.

Referring first to FIG. 1, a block diagram of a typical satellitecommunications system is shown. The satellite communications system 10includes a first communications terminal or a gateway station 24 (alsoreferred to as a base station), second communications terminal or mobileterminal 12 (also referred to as a wireless terminal or wirelesstransceiver), a public switched telephone network (PSTN) 22, a satellite26, and communications links 28 and 30. The satellite communicationssystem 10 is one embodiment in which the present invention may bepracticed. It is noted that the terms communications terminal, terminal,and transceiver are used synonymously.

The public switched telephone network (PSTN) 22 is coupled to thegateway station 24 in a conventional manner, using, for exampleconventional wire-based, land-based or land-line connections. Thegateway station 24 is coupled to the satellite 26 through a firstcommunications link 28, and the satellite 26 is coupled to the mobileterminals through communications link 30.

In practice, voice communications take place between the mobile terminal12 and the PSTN 22 via the gateway station 24 and the satellite 26. Assuch, the PSTN 22 switches the voice communications to the gatewaystation 24 to be transmitted to the mobile terminal 12 via the satellite26, as is conventionally done. As earlier described, the mobile terminal12 is frequently placed in positions in which it cannot maintainsynchronization with a satellite 26. For example, the mobile terminal 12might be turned off and stored, may be carried into a building withsignificant signal attenuation, or may be newly purchased. In any case,the mobile terminal 12 must be able to find the waveform (also referredto as a synchronization signal) sent from the gateway station 24 via thesatellite 26 to synchronize with the timing and frequency of thecommunications link 30 prior to being able to begin communication. Thus,as is known in the art and shown in FIG. 1, the gateway station 24transmits the waveforms to all mobile terminals 12 within coverage ofthe satellite 26. The waveforms in a conventional satellitecommunications system 10 are transmitted in short duration continuouswave bursts (“bursts”) 20 between the gateway station 24 and thesatellite 26, and in burst 16 between the satellite 26 and the mobileterminal 12 in a variety of conventional schemes. The satellite 26relays the burst 20 to mobile terminal 12 for synchronization by anacquisition system in the mobile terminal 12.

As the bursts 16 and 20 propagate through air and other interceptingmedia along a direct line-of-sight or other multi-paths resulting fromscattering due to reflection and diffraction of signals contained withinthe bursts 16 and 20 the signals become distorted and attenuated due tomany different factors as described further with reference to FIG. 2.

In accordance with one embodiment of the present invention, a waveformthat addresses the concerns of the prior art, known as the compositewaveform (also referred to as the composite signal waveform), istransmitted from the gateway station 24 to mobile terminals 12. Oneexample of a composite signal waveform is a dual-chirp waveformdescribed below. The composite waveform, e.g. the dual-chirp waveform isdiscussed in detail with reference to FIGS. 3 through 6D. Furthermore,in accordance with another embodiment of the present invention, a novelacquisition section is present in the mobile terminal 12 that is used toacquire the composite waveform and extract both timing and frequencyoffsets of the received composite waveform. The acquisition section isdiscussed in more detail with reference to FIGS. 7 through 10.

Referring next to FIG. 2, a functional block diagram is shown of howcontributions to a signal waveform (or waveform) are added as an initialsignal s(t) (or “source signal” or “transmitted signal”) is propagatedfrom a source transmitter 32 (e.g. the transmitter of the gatewaystation 24 of FIG. 1) to a receiver 44 (e.g. the receiver of the mobileterminal 12 of FIG. 1). The initial signal, or source signal, s(t) issent by the source transmitter 32 and incurs time delay 34 due to a timedelay “t₀” during propagation of the signal from the source transmitter32 to the receiver 44.

As previously described in the background herein, time delays resultfrom several factors. Time delays may be caused by obstructions in thesignal path that generate “multi-paths” from scattering due toreflections and diffractions of the signal from the obstructions. Thedifferences in distance between the multi-paths result in time delayoffsets as well as fading of the signal, depending upon the channel(e.g. Rician or Rayleigh fading).

Also, in a satellite communications system, such as shown in FIG. 1,relative motion may exist between the satellite (i.e. source transmitter32) and the mobile terminal 12 (i.e. receiver 44) due to the relativevelocity of the satellite as it orbits the Earth and another velocity ofthe mobile terminal as it operates from a moving vehicle, for example,results in varying time delays by the signals traveling there between.These timing delays all contribute to the time delay of t₀ asrepresented by time delay 34.

An additional source of signal attenuation is a frequency offset asrepresented as frequency offset 36. Frequency offsets of the carrierfrequency of the source signal s(t) in satellite communications systemsare primarily due to Doppler occurring from relative motion of thesource transmitter 32 and the receiver 44. As the source transmitter 32and the receiver 44 move toward one another, the received carrierfrequency appears to shift higher; as they move away from one another,the received carrier frequencies appear to shift lower. Thus, afrequency offset 36 is introduced into the source signal s(t). Thefrequency offset 36 is represented mathematically by multiplying, atmultiplier 38, the source signal s(t) with a complex waveform such asrepresented by exp(j2πf_(d)t), wherein f_(d) is the doppler frequencyoffset in Hertz and t is time in seconds.

Thus, as in known in the art, these contributions of time delay 34 andfrequency offset to the source signal s(t) require that an acquisitionsystem of a mobile terminal 12 resolve these contributions before beingable to properly acquire the source signal and thus, synchronize with atransmitter 32.

Additionally, noise contributions n(t) 40, such as Additive WhiteGuassian Noise (AWGN), are represented in hardware terms bymathematically adding a low-level waveform n(t) exhibiting Guassiancharacteristics, by the adder 42. The source signal s(t) shown,therefore, represents a signal which is a true signal (i.e. undistortedby the channel through which the signal is transmitted) transmitted bythe source transmitter 32, represented in continuous time t wherein t=0at a start of the burst. Thus, as can be seen in FIG. 2, at the receiver44, a received signal r(t) may be represented as r(t)=s(t−t₀)e^((j(2πf)^(d) ^(t)+φ))+n(t), wherein t₀ is the time delay in seconds, f_(d) isthe Doppler frequency offset in Hertz and φ is a random phase offset.Thus, r(t) equates to a phase shifted version of s(t), including randomphase.

In accordance with the invention herewith, a waveform used forsynchronization must be transmitted from the gateway station 24 (sourcetransmitter 32) to the mobile terminal 12 (receiver 44), wherein themobile terminal can easily detect the waveform and resolve the frequencyoffset and timing offset in the presence of noise.

The Composite Waveform

Referring next to FIG. 3, a plot of amplitude versus time for acomposite waveform is shown in accordance with one embodiment of thepresent invention, which is shown as a dual-chirp waveform that includesa combined up-chirp waveform and a down-chirp waveform, which may betransmitted by the gateway station 24 to the mobile terminal 12 via thesatellite 26 of the satellite communication system 10 of FIG. 1. Thecomposite waveform (also referred to as a composite signal waveform) isshown at transmission and thus, prior to experiencing frequency offsets,timing offsets, and noise during transmission through the communicationslink. The dual chirp waveform 50, which is one example of a compositewaveform consistent with this embodiment of the present invention,provides a waveform for synchronization, that addresses the needs of theprior art as described above.

This example of a composite waveform is referred to as a dual-chirpwaveform 50 because it is a composite waveform consisting of twocomponent waveforms: an up-chirp waveform and a down-chirp waveform. Achirp waveform, as known in the art, is a signal in which the frequencychanges linearly over the duration of the waveform. In other words, thefrequency is “swept” (i.e. the frequency varies with time) across theduration of the chirp waveform. This is in contrast to a sinusoidal or“tone” waveform in which the frequency remains constant throughout theduration of the waveform making it susceptible to “spurs” in thereceiver of the mobile terminal as described above.

The dual-chirp waveform 50 is a composite of an up-chirp waveform and adown-chirp waveform. In operation, the up-chirp waveform has a frequencythat increases linearly with time, while the down-chirp waveform has afrequency that decreases linearly with time (see FIG. 4 whichillustrates a frequency versus time plot for the dual-chirp waveform50). Advantageously, the frequency of the up-chirp waveform and thedown-chirp waveform vary oppositely with respect to time.

The up-chirp waveform begins with an initial frequency (e.g. having afrequency offset relative to a carrier frequency) of a firstpredetermined frequency offset (e.g. f_(c) −7500 Hz). During each burst,the initial frequency of the up-chirp waveform increases linearly toreach an ending frequency offset value of the initial frequency (e.g.f_(c) +7500 Hz) by an end of the burst. Similarly, the down-chirpwaveform begins at an initial frequency that is the ending frequency ofthe up-chirp waveform (e.g. f_(c) +7500 Hz) which decreases linearlyuntil it reaches it's ending frequency (e.g. f_(c) −7500 Hz), which isthe initial frequency of the up-chirp waveform. This frequencyrelationship is more easily seen in the frequency versus time plot shownin FIG. 4.

Separately, both the up-chirp waveform and the down-chirp waveform arerepresented mathematically on a complex plane, and may be referred to as“complex waveforms”. Thus, both the up-chirp waveform and the down-chirpwaveform may be represented mathematically as having a real componentand an imaginary component. Advantageously, the upchirp waveform and thedownchirp waveform are transmitted simultaneously and are “in sync” witheach other, i.e. the down-chirp waveform starts at a frequency at whichthe up-chirp waveform ends, that is, e.g. +7500 Hz, and ends at e.g.−7500 Hz. Thus, the down-chirp waveform is the complex conjugate of theup-chirp waveform. As such, in the dual-chirp waveform, the imaginarycomponents of the up-chirp waveform and the down-chirp waveform cancelout, the dual chirp waveform 50 is represented completely by a realcomponent. Therefore, the dual-chirp waveform 50, is representedmathematically on a real plane, and may thus be referred to as a “realwaveform”, as shown in FIG. 3 as a composite of an up-chirp waveform anda down-chirp waveform.

For various reasons, which will be discussed more with reference to FIG.4 and throughout the specification, the dual-chirp waveform is oneexample of a composite waveform of two simultaneously transmittedwaveforms having a known frequency variation, i.e. the frequency varieslinearly with time. The dual-chirp waveform 50 has preferred properties,making it a preferred choice as a waveform for synchronization forseveral reasons. Since both frequency variations of the up-chirpwaveform and the down-chirp waveform are known and are opposite of eachother, both a frequency offset f_(d) and a time delay t₀ of the receivedsignal r(t) can be estimated by solving for two (2) equations with twounknowns in an acquisition section of a mobile terminal as is describedin more detail with reference to FIG. 7.

Referring next to FIG. 4, a frequency versus time plot is shown of thedual-chirp waveform 50 of FIG. 3, which illustrates the two componentwaveforms, i.e. the up-chirp waveform 60, wherein frequency increaseslinearly with time, and a simultaneously transmitted down-chirp waveform62, wherein frequency decreases linearly with time. FIG. 4 illustratesthe linearly increasing or decreasing frequency with time of eachrespective waveform.

The up-chirp waveform 60 and the down-chirp waveform 62 of the compositedual-chirp waveform 50 can be expressed mathematically. In terms of thesignals shown in FIG. 2, the source signal s(t) that is transmitted, asa burst containing the dual-chirp waveform of FIG. 3, from the gatewaystation 24 to the mobile terminal 12, with respect to continuous time t,wherein t is defined with respect to a start of a burst of duration T,(i.e. t=0 at the start of the burst), then the transmitted signal s(t)is defined by equation (1):s(t)=s₁(t)+s ₂(t)  (1)p(t)[e ^(jπK(t−T/2)) ² +e ^(−jπK(t−T/2)) ² ]  (2)wherein s₁(t) represents an up-chirp waveform of frequency f₁(t) ands₂(t) represents a down-chirp waveform of frequency f₂(t), T is theduration of the dual-chirp waveform in seconds, p(t) is a windowdefining an envelope of the signal in time (also referred to as aramping function such that within the window of time p(t)=1 and at timesoutside of the window of time p(t)=0), and whereinf ₁(t)=K(t−T/2), and  (3)f ₂(t)=−K(t−T/2)  (4)where K is sweeping rate parameter (i.e. the rate at which the frequencyis “swept” across the duration of the burst or the “slope” of the linespresenting the up-chirp waveform and the down-chirp waveform) orfrequency rate-of-change of f₁(t) and f₂(t) respectively. As shown inFIG. 4, K is the slope of the up-chirp waveform 60 and −K is the slopeof the down-chirp waveform 62. In alternative composite waveforms, Kdoes not have to be the same for each component waveform.

There are several reasons why a composite waveform, such as thedual-chirp waveform 50 as shown in FIGS. 3 and 4 overcomes the concernsof prior art waveforms used for synchronization. First, advantageously,the transmitted dual-chirp waveform easily lends itself to detection ata mobile terminal, for example, using a Fast Fourier Transform (FFT).This process is further described with reference to FIGS. 7–10. Inpractice, an FFT enables acquisition to be performed in real-time withfirmware/hardware, as is done in some types of prior art waveforms, suchas a waveform that consists of a tone followed by a modulated waveformas described above. Thus, the ability to detect the dual-chirp waveform50 using an FFT is a desirable feature and one driver for the presentinvention.

Furthermore, by looking at a received dual-chirp waveform 50 containedin the received signal r(t) of FIG. 2, acquisition systems at thereceiver 44 of FIG. 2 (e.g. mobile terminal 12) employing an FFT canidentify the dominant frequency components of both the deswept up-chirpwaveform 60 and down-chirp waveform 62, which is then used to estimatethe frequency offset f_(d) (i.e. the Doppler frequency offset) and thetime offset t₀ (i.e. timing delay), in the received dual-chirp waveform.This is enabled since the up-chirp waveform 60 and the down-chirpwaveform 62 each will be received with an unknown frequency offset f_(d)and an unknown timing offset t₀. Furthermore, each component waveformcan be expressed mathematically as a relationship including thefrequency offset, timing offset, and the frequency estimated by the FFT.Thus, the two component waveforms of the dual-chirp waveform willprovide two equations and two unknowns (f_(d), t₀) if the peak frequencyestimates (obtained with an FFT) of both the up-chirp waveform 60 andthe down-chirp waveform 62 are determined by a search algorithm. Thus,f_(d) and t₀ can be solved. This method enables a reduction in theamount of synchronization information needed as compared with the use ofpure sinusoids or tones in the FCCH. The FFT and the frequency offsetand timing offset estimations are further described below with referenceto FIGS. 7–10.

Additionally, the dual-chirp waveform 50 does not resemble a “tone” or asinusoid having a constant frequency; thus, the problem of “spurs”introduced into the signal waveform at the receiver (e.g. mobileterminal 12) are overcome.

Also, the dual-chirp waveform illustrated in FIGS. 3 and 4 can supportan “alerting” operation when a satellite communications system such asshown in FIG. 1 needs a robust mechanism to provide synchronization withacceptable degradation. The sweep parameter or slope K of the up-chirpwaveform 60 and down-chirp waveforms 62 controls a trade-off betweentiming accuracy and signal bandwidth. Higher values of K increase theaccuracy of the timing estimate; however, the value of K is limited bythe available bandwidth of the channel. However, in reality there is afrequency uncertainty involved, due to the local oscillator in themobile terminal 12, so realistically the value of K is even furtherlimited to less than the available bandwidth of the channel.

Additionally, the dual-chirp waveform 50 of FIGS. 3 and 4 also supportssignal-to-noise (SNR) estimation and provides significantly better SNRresults than estimates using data modulated waveforms at low SNR's. Thisadvantage results from the receiver's knowledge of the expectedwaveform, unlike unknown data modulated waveforms, since the mobileterminal is configured to know what the composite waveform. e.g.dual-chirp waveform 50, should look like.

This better SNR estimation provides more accurate channel statedetermination, in turn. Assuming dual-chirp waveforms of duration equalto 112 data bearing symbols, the dual-chirp waveform 50 can supportnormal data and control traffic operating at typical values of +6 dBE_(s)/N₀ (i.e. SNR), alerting operations at −8 dB Es/N₀, tracking ataround −15 dB E_(s)/N₀, and E_(s)/N₀ estimation at around −20 dBE_(s)/N₀. This is a significant improvement in versatility since thedual-chirp waveform advantageously supports both voice and datacommunications and supports other services, such as alerting, by usingthe same signal waveform. As earlier stated, prior art systems must sendseparate waveforms to support voice/data communications and alerting.

It is important to note that the dual-chirp waveform 50 shownspecifically in FIGS. 3 and 4 is only one example of a compositewaveform that can be used as a synchronization signal sent from thegateway station to a mobile terminal of a satellite communicationssystem, for example. Other types of composite waveforms could also beused. There are three main design parameters, which will be described,that would define such composite waveforms, such as the dual-chirpwaveform, for example.

The first design characteristic for the composite waveform is that thecomposite waveform should be a composite of two or more componentwaveforms that each have frequency that varies with time (i.e. f₁(t),f₂(t), . . . f_(n)(t), where n is the number of waveforms) that aresimultaneously transmitted from the gateway station. Although, more thantwo waveforms may be used, two waveforms is the most efficient in termsof processing at the acquisition system of the mobile terminal.Furthermore, the frequencies of the two or more component waveforms donot have to vary linearly with time (as the dual-chip waveform does) orvary at the same rate, e.g. the slope or K is different for thedifferent component waveforms.

The second design characteristic of the composite waveform is that therange of values of the frequencies of the component waveforms should beas large as possible. Thus, the bandwidth of f₁(t) and the bandwidth off₂(t) should be as large as possible while considering the availablebandwidth of the channel. For example, if the available bandwidth of the23.4 kHz channel is 18 kHz (allowing for both the channel bandwidth andthe carrier uncertainty in the receiver, e.g. local oscillator, of themobile terminal), the bandwidth of the component waveforms should begreater than half (50%), or ideally greater than 80%, of the availablebandwidth of the channel (e.g. 15 kHz is greater than 9 kHz), but wouldstill work at as low as 10% of the available bandwidth of the channel(e.g. greater than 1.8 kHz). Shown in FIG. 4, the range of values off₁(t), which is the up-chirp waveform 60, is from f_(c)−7500 Hz tof_(c)+7500 Hz (total bandwidth 15 kHz of an available bandwidth of 18kHz) and the range of values of f₂(t), which is the down-chirp waveform62, is from f_(c)+7500 Hz to f_(c)−7500 Hz (total bandwidth 15 kHz of anavailable bandwidth of 18 kHz). The lower the bandwidth of the componentwaveforms is, the more the component waveforms resemble “tones” to whichunmodulated spurs at the receiver become an issue.

And the third design characteristic for the composite waveform is thatthe range of values for the differences between the instantaneousfrequencies of the component waveforms should be as great as possible.This concept relates to FIG. 4 in that the slope of up-chirp waveform 60(i.e. K₁ in Eq. (3)) and the slope of the down-chirp waveform 62 (i.e.K₂ in Eq. (4)) should be as different as possible. As an example, asshown in FIG. 4, at point “A”, the difference between f₁(t) and f₂(t) isabout −15 kHz. At point “B”, the difference between f₁(t) and f₂(t) isabout −12 kHz. At point “C”, the difference between f₁(t) and f₂(t) isabout −8 kHz. And at point “D”, the difference between f₁(t) and f₂(t)is about −4 kHz. At point “E”, the difference between f₁(t) and f₂(t) isabout 0 kHz. At point “F”, the difference between f₁(t) and f₂(t) isabout +4 kHz. At point “G”, the difference between f₁(t) and f₂(t) isabout +8 kHz. At point “H”, the difference between f₁(t) and f₂(t) isabout +12 kHz. And at point “C”, the difference between f₁(t) and f₂(t)is about +15 kHz. Thus, the range of values for the difference betweenthe instantaneous frequencies of the up-chirp waveform 60 and thedown-chirp waveform 62 varies between −15 and +15 kHz, for a total rangeof 30 kHz. Note that even though the magnitude of the slope of the twocomponent waveforms is the same, they are opposite in direction.

In contrast, a composite waveform that would violate the third designcharacteristic would be the composite waveform shown in FIG. 4A thatincludes two down-chirp waveforms, first down-chirp waveform 70 andsecond down-chirp waveform 72 (referring briefly to FIG. 4A). Note thatat points “A′, B′, C′, and D′”, the difference between the instantaneousfrequencies of the first down-chirp waveform 70 and the seconddown-chirp waveform 72 is about 10 kHz at each point. Thus, the range ofvalues for the differences is essentially zero (i.e. the differencesvary between −10 kHz and −10 kHz). This type of composite waveform wouldbe easily detectable with an FFT in an acquisition, but would not yieldaccurate estimates of the frequency offset and timing offset that areneeded for accurate synchronization of the mobile terminal to thegateway station. Each waveform would yield a mathematical expressionhaving two unknowns, and thus, there would be two equations and twounknowns. However, the information would be of little use insynchronization because the two waveforms would give approximately thesame two equations having the same two unknowns. Ideally, the twoequations are very different from each other.

It has been found that the range of the values of the differences of theinstantaneous frequencies of the two component waveforms should ideallybe a range of values equal to or greater than at least 10%, preferablyat least 50%, and ideally at least 80%, of twice the available frequencybandwidth of the channel. For example, the range of values for thedifferences of the instantaneous frequencies of the up-chirp waveform 60and the down-chirp 62 of the dual-chirp waveform 50 as shown in FIG. 4 arange between −15 kHz and +15 kHz, or a total range of 30 kHz, which ismuch greater than 10% (e.g. 3.6 kHz), 50% (e.g. 18 kHz), or even ideally80% (e.g. 28.8 kHz) of twice the available bandwidth of the channel(e.g. 36 kHz, which is 2×18 kHz).

It is also noted that the component waveforms of such a compositewaveform used for synchronization do not have to vary linearly withtime, or even intersect on a frequency versus time plot as does thedual-chirp waveform 50 of FIG. 4. Thus, the composite waveform be anycomposite waveform that meets the above stated three design parameters.These three design parameters will be discussed further throughout thespecification. Furthermore, as described later in the specification, itwill become apparent that the dual-chirp waveform 50 is a preferredembodiment. The distinct advantages of the dual-chirp waveform 50 overother composite waveforms that fit within the three design parameterswill be explored also below.

Referring next to FIGS. 5A through 5D, shown are illustrations of afrequency versus time plot of the transmitted dual-chirp waveform (ofthe embodiment shown in FIGS. 3 and 4) including the combined up-chirpwaveform and down-chirp waveform that is transmitted from the gatewaystation 24 to the mobile terminal 12 of the satellite communicationssystem of FIG. 1, and how the received dual-chirp waveform is effectedby frequency and timing offsets.

First referring to FIG. 5A, a frequency versus time plot is shown of thetransmitted dual-chirp waveform 80 of the embodiment shown in FIGS. 3and 4, including the combined up-chirp waveform and down-chirp waveformas earlier described above. Additionally, in FIG. 5A, the dual-chirpwaveform 80 represents the received dual-chirp waveform in idealconditions with no frequency or timing offsets. Thus, the transmittedsource signal (i.e. transmitted dual-chirp waveform 80) equals thereceived signal (i.e. the received dual-chirp waveform 80); therefore,s(t)=r(t) from FIG. 2. Note that for illustration purposes, the effectsof noise are neglected.

Next referring to FIG. 5B, an illustration is shown of a frequencyversus time plot of the transmitted dual-chirp waveform 80 of FIG. 5Aand the corresponding received dual-chirp waveform 82 (dashed line) thatis received at the mobile terminal 12 of FIG. 1, wherein a frequencyoffset f_(d) only (no timing offset) has been introduced into thereceived dual-chirp waveform 82. Note that in reality the receiveddual-chirp waveform 82 will be effected by noise (i.e. noise 40 of FIG.2) and will appear distorted instead of as the straight and undistorteddashed lines of FIG. 5B. For illustration purposes, straight andundistorted dashed lines are used for the received dual-chirp waveform82.

Next referring to FIG. 5C, an illustration is shown of a frequencyversus time plot of the transmitted dual-chirp waveform 80 of FIG. 5Aand the corresponding received dual-chirp waveform 82 (dashed line),wherein a timing offset to only (no frequency offset) has beenintroduced into the received dual-chirp waveform 82.

Next referring to FIG. 5D, an illustration is shown of a frequencyversus time plot is shown of the transmitted dual-chirp waveform 80 ofFIG. 5A and the corresponding received dual-chirp waveform 82 (dashedline), wherein both a frequency offset f_(d) and a timing offset t₀ havebeen introduced into the received dual-chirp waveform 82. Thisillustration is the most common result in that both a frequency andtiming offset have been introduced into the received dual-chirp waveform82. However, the receiver of the mobile terminal does not know eitheroffset. Thus, the use of two component waveforms, the up-chirp waveformand the down-chirp waveform provide a means for accurate estimation ofboth timing and frequency offset. For example, the received up-chirpwaveform mathematically yields, through the use of a FFT, a singleequation having two unknowns, e.g. f_(d) and t₀ and the frequency of thepeak of the received up-chirp waveform (obtained in an FFT described inFIG. 7). Similarly, the received down-chirp signal mathematicallyyields, through the use of a FFT, a different single equation having twounknowns, e.g. f_(d) and t₀ and an estimate of the peak frequency of thedown-chirp waveform (from the FFT, as described in FIG. 7). Therefore,both the frequency offset and the timing offset can be accuratelyestimated as will be described in more detail with reference to FIGS. 7though 10.

In contrast to frequency versus time plots of FIGS. 5A through 5D, thefrequency versus time plots of FIGS. 6A through 6D show a compositewaveform that does not meet the third design parameter as describedabove, and thus, will not be able to distinguish between the frequencyand timing offsets.

Referring next to FIG. 6A, an illustration is shown of a frequencyversus time plot of a transmitted composite waveform 90 that would notprovide accurate frequency and timing offset estimations at the mobileterminal, in contrast to the composite waveforms meeting the threedesign parameters, e.g. the dual-chirp waveform 50 as shown in FIGS. 3through 5D. The transmitted composite waveform 90 includes twodown-chirp waveforms wherein the range of differences between theinstantaneous frequencies of the two individual down-chirp waveforms ofthe composite signal waveform 92 over the duration of the compositesignal waveform 92 is not large. As shown and further described withreference to FIG. 4A, this range of values is actually zero.

Referring next to FIG. 6B, a frequency versus time plot is shown of thetransmitted composite signal waveform 90 of FIG. 6A and thecorresponding received composite signal waveform 92 (dashed line) thatwould be received at the mobile terminal, wherein a frequency offsetf_(d) has been introduced into the received composite signal waveform92.

Referring next to FIG. 6C, a frequency versus time plot is shown of thetransmitted composite signal waveform 90 of FIG. 6A and thecorresponding received composite signal waveform 92 (dashed line),wherein a timing offset t₀ has been introduced into the receivedcomposite signal waveform 92.

Referring next to FIG. 6D, a frequency versus time plot is shown of thetransmitted composite signal waveform 90 of FIG. 6A and thecorresponding received composite signal waveform 92 (dashed line),wherein both a frequency offset f_(d) and a timing offset t₀ have beenintroduced into the received composite signal waveform 92. In operation,the receiver of the mobile terminal will be able to detect the receivedcomposite signal waveform and estimate a peak frequency of the twodown-chirp waveforms using an FFT; however, the receiver will be unableto accurately estimate f_(d) and t₀. This is because each individualdown-chirp waveforms will mathematically yield, through the use of aFFT, a single equation having two unknowns, e.g. f_(d) and t₀ and theknown (estimated) peak frequency of both down-chirps. However, eachequation essentially provides the same information and thus, is noteffectively solvable for the two unknowns, f_(d) and t₀.

Acquisition of the Composite Signal Waveform

This section deals with the acquisition of the composite waveform,specifically the dual-chirp waveform described above, that sent from thegateway station to the mobile terminal via the satellite in thesatellite communications systems of FIG. 1 and used for synchronizationpurposes. Thus, the acquisition process involves searching for thecomposite waveform at the mobile terminal in an acquisition system ofthe mobile terminal.

Referring next to FIG. 7, a block diagram is shown of an acquisitionsystem as may be employed e.g. in a mobile terminal 12 of FIG. 1 foracquiring composite waveforms sent as bursts and received having thedistortions described by FIG. 2, including frequency and timing offsets(see FIG. 5D) and also including the effects of noise. The acquisitionsystem 100 comprises an antenna 102 coupled at an output to an input ofan RF interface electronics 104, which is coupled at an output to aninput of a matched filter 106, e.g. a Square Root Raised Cosine (SRRC)matched filter. The matched filter 106 output is coupled a buffer 120which is coupled to both a first phase shifter 108 and a second phaseshifter 110. The first phase shifter 108 and the second phase shifter110 are each coupled at respective outputs, to an input of a first FFTprocessor 112 and an input of a second FFT processor 114. A BurstDetection and Parameter Estimation Processor 116 (hereinafter referredto as the detection and estimation processor 116) receives, as oneinput, the output from the first FFT Processor 112, and as anotherinput, the output from the second FFT Processor 114. Furthermore, thedetection and estimation processor 116 includes a control signal 118back to the buffer 120. Also, the detection and estimation processor 116includes a burst detector (not shown), a parameter estimator (notshown), and a Discrete Fourier Transform (not shown).

Also shown in FIG. 7 are frequency vs. time plots 122, 128, 132, 142,148, and 152 of the waveforms at various points and frequency vs.magnitude of an FFT plots 138 and 158 and in the acquisition system.Furthermore, first path 107 and second path 109 are shown. The firstpath 107 is represented as the path taken by a sampled signal going fromthe buffer 120 to the first phase shifter 108, then to the first FFTprocessor 112, and finally to the detection and estimation processor116. The second path 109 is represented as the path taken by a sampledsignal going from the buffer 120 to the second phase shifter 110, thento the second FFT processor 114, and finally to the detection andestimation processor 116.

In practice, the antenna 102 receives a burst from a FCCH logicalchannel, which the gateway station has been configured to transmit aburst containing a composite waveform according to one embodiment of thepresent invention. In this particular embodiment, the composite waveformcomprises a dual-chirp waveform as described above with reference toFIGS. 3–4 and 5A–5D. Also, in this embodiment, the dual-chirp waveformis a burst having a length of 5 msec that is transmitted every 320 msecby the gateway station.

During acquisition at the mobile terminal, the acquisition system 100searches a defined set of carriers (e.g. searches 10 channels ofapproximately 1000 available channels) for the burst containing thedual-chirp waveform. As earlier described, once found, the dual-chirpwaveform is used to determine the frequency offset and timing offset ofthe received dual-chirp waveform, which is used to compute the carrierfrequency and frame timing information for communications back to thegateway station from the mobile terminal via the satellite. Thus, themobile terminal has completed acquisition and the mobile terminal is nowsynchronized with the gateway station. As earlier explained, thedual-chirp waveform happens to be “real” in that a baseband equivalentwaveform is represented mathematically in one single dimension, incontrast to how Quadrature Phase Shift Keying (QPSK) baseband waveformsare represented.

In one preferred embodiment, an initial burst is received in analog formby the antenna 102, is transformed into digital format by the RFinterface electronics 104, which may employ any type of standard A/Dconversion methods or means known in the art.

Then, the matched filter 106, such as an SRRC matched filter 106,filters the output of the RF interface electronics 104 and the buffer120 samples the digital time-domain samples, i.e. complex in-phase (I)and quadraphase (Q) digital samples, from the received burst containingthe dual-chirp waveform and stores them. The buffer 120 samples thedigital time-domain samples at the output of the matched filter 106 at asample frequency f_(s), e.g. 46.8 kHz. This equates to 234 digitaltime-domain samples taken at 46.8 kHz during the 5 msec duration of thedual-chirp waveform.

The digital time-domain samples, complex I and Q samples, sampled by thebuffer 120 are split into two paths, shown as the first path 107 and thesecond path 109. First, the digital time-domain samples, represented asr(t) in FIG. 7, are sent along the first path 107 to the first phaseshifter 108 in order to isolate the up-chirp waveform. At this point,the samples are not yet sent along the second path 109. This is doneonly after the up-chirp waveform is detected in the first path 107.

A frequency vs. time plot 122 of r(t), the digital samples output fromthe buffer 120, is shown. Advantageously, this plot 122 is shown asactually containing the received dual-chirp waveform including theeffects of noise (indicated as uneven, distorted lines instead ofstraight lines shown earlier in FIGS. 4 through 5A) and including anunknown frequency and timing offset. The frequency vs. time plot 122illustrates both the up-chirp waveform 124 and the down-chirp waveform126. The unknown frequency and timing offsets are represented in FIG.5D.

Note that for illustration purposes to show how the dual-chirp waveformis detected in the acquisition system 100, it is presumed that the burst(a set of time domain digital samples) that has been sampled at thebuffer 120 of the mobile terminal is the full dual-chirp waveform.However, the mobile terminal must “search” for the 5 msec dual-chirpwaveform that occurs every 320 msec over a variety of frequencies usingthe sliding search window as described below. Thus, most of the time,the burst sampled at the buffer 120 is just random noise or a portion ofthe dual-chirp waveform, not the full dual-chirp waveform shown infrequency vs. time plot 122 at the output of the buffer 120 in the firstpath 107. As such, each set of digital time-domain samples sampled atthe input buffer 120 is called a hypothesized waveform, since theacquisition system 100 is hypothesizing that the composite waveform iscontained within the set of samples at the buffer 120.

It is important to note that first path 107 is used to detect one of thetwo component waveforms of the composite waveform. In the case of thedual-chirp waveform, the acquisition section is looking for the up-chirpin the first path 107, but could be configured to look for thedown-chirp waveform if desired. Thus, the acquisition system 100 ishypothesizing that the signal within the buffer 120 is the dual-chirpwaveform. Next, the signal output from the matched filter 106 is“deswept” at the first phase shifter 108, which is typically amultiplier, by multiplying the signal r(t) by a first desweepingwaveform. The first desweeping waveform is the complex conjugate of thecomponent waveform that the acquisition system is attempting to find inthe first path 107 (i.e. the up-chirp waveform). Thus, in this case, thefirst desweeping waveform 130 is the complex conjugate of the up-chirpwaveform, which advantageously happens to be the down-chirp waveform ofthe dual-chirp waveform 130, shown as exp(−jk(t−T/2)²). A frequency vs.time plot 128 is shown that represents the first desweeping waveform130. The first desweeping waveform 130 may also be referred to as afirst hypothesizing waveform since it is being used to “hypothesize” anup-chirp waveform in the received waveform.

Since multiplication in the time-domain is addition in the frequencydomain, the result of such desweeping at the first phase shifter 108 isshown as the frequency vs. time plot 132 in which the frequency of thereceived up-chirp waveform 134 is now simply leveled out or “deswept”into a “tone” that includes noise (also referred to as a narrow bandwaveform), and the phase shifted down-chirp waveform 136 has undergone adoubling of its slope, thus, the signal has been phase shifted. Notethat any spurs present in the RF interface electronics 104 will nolonger be tonal in nature due to the desweeping process.

The term “deswept” is used because the first desweeping waveform 130 isdesigned to desweep or flatten out the frequency vs. time plot of one ofthe component waveforms of the composite waveform (turn it into anarrowband waveform); in this case, the up-chirp waveform (i.e.frequency is swept over time) so that the frequency of the up-chirpwaveform does not change linearly with time and results in a desweptup-chirp waveform that has approximately a constant frequency, like a“tone”. The other component waveform of the composite signal waveform,for example, the down-chirp waveform component of the dual-chirpwaveform, is amplified (in frequency) and isolated from the desweptup-chirp waveform 134 (now a tone waveform including noise), so that thedetection and estimation processor 112 can be used to detect the “tone”of the deswept up-chirp waveform.

Furthermore, the desweeping at the first phase shifter 108 can beimplemented by a computer program in a software implementation, or infirmware or hardware in alternate embodiments. For example, usingsoftware or firmware, if the buffer 120 output (complex I and Q outputs)are initially B_I(n) and B_Q(n), n being a sample number, then for n=0to 233, the filtered and buffered output is represented by:B_I(n)+jB_Q(n). Furthermore, if the up-chirp conjugate is representedusing table coefficients α and β, then the conjugate is [α(n)+j β(n)].

Next, the deswept component waveform (shown as the deswept up-chirpwaveform 134 in frequency vs. time plot 132) is sent to the first FFTProcessor 112 to be Fast Fourier transformed into an initialfrequency-domain signal. In the embodiment shown, wherein the dual-chirpwaveform is 5 msec in length and the buffer 120 samples 234 digitalsamples, a “256 point FFT” is used in the first FFT processor 112. Thus,as is known in the art, a zero padder (not shown) within the first FFTprocessor 112 is used to zero pad the last 22 samples for the 256 pointFFT, i.e. set the last 22 samples equal to zero. Thus, the first 234samples (n=0 to n=233) of phase shifted digital time domain samples aresent to the 256 point FFT, and the last 22 samples (n=234 to n=255) areset to zero and sent to the 256 point FFT of the up-chirp FFT processor112. In different embodiments, a zero padder may be unnecessary or adifferent size FFT may be used depending on the size of the dual-chirpwaveform and the number of samples taken at the buffer 120.

The first FFT processor 112 transforms the phase-shifted, zero-padded Iand Q samples or output from the first phase shifter 108, which are intime-domain, into frequency domain I and Q samples, as is known in theart. A frequency vs. magnitude plot 138 is shown of the output of thefirst FFT processor 112 which extracts and isolates the deswept up-chirpwaveform 134 or tone indicated by the peak 140 of the plot 138. Thispeak 140 of the plot 138 may be referred to as frequency representationof the deswept up-chirp waveform 134.

The resulting signal is sent from the first FFT processor 112 to thedetection and estimation processor 116 which is used to detect thepresence of a peak 140, or frequency representation of the desweptup-chirp waveform 134, which indicates the presence of the up-chirpwaveform 124 of the dual-chirp waveform as described above.

In order to detect an actual up-chirp waveform (represented at thispoint as the frequency representation of the deswept up-chirp waveform140 or peak 140) in the received digital samples, the detection andestimation processor 116 searches the output of the first FFT processor112 by comparing a signal-to-noise ratio (i.e. SNR) of the output of thefirst FFT processor to an SNR Threshold. A signal-to-noise ratio (SNR)is next computed from a ratio of signal-power/noise-power. A SNR iscalculated by determining a maximum power among all frequency binscontaining output from the first FFT Processor 112, as detailed in thefollowing description.

In calculating the SNR, first, a Bin Power is calculated for all of thefrequency bins by adding the squares of the frequency domain I samplesto the squares of the frequency domain Q samples for each sample n.

A Maximum Power Bin of location m is determined from amongst all the binpowers. The SNR is next computed by adding energies (Bin Powers) of bins(m−1) through bins (m+1). A Noise Power is computed as a sum ofremaining power from remaining bins, i.e. all bins except for theremaining bins wherein n={(m−1), m, (m+1)}. Also, there are unlimitedother methods of computing an SNR known in the art, any of which may beemployed herewith in accordance with the principles of this invention.

Next, the computed SNR is compared against a computed SNR Thresholdresulting in one of two scenarios. In the first scenario, if thesignal-to-noise ratio (SNR) computed exceeds the SNR threshold, then thedetection and estimation processor 116 knows that it has received thecomposite signal waveform, e.g. the dual-chirp waveform, since thefrequency representation of the deswept up-chirp waveform will cause theSNR threshold to be exceeded. Once exceeded, the detection andestimation processor has found the up-chirp component waveform of thedual-chirp waveform. Alternatively, in the second scenario, if thecomputed SNR does not exceed the SNR threshold, i.e. there is no peak140, then the detection and estimation processor knows that it has notreceived the composite signal waveform, e.g. the dual-chirp waveform.

More specifically, in the second scenario, if an up-chirp waveform, i.e.the frequency representation of the deswept up-chirp waveform or tone,is not detected (i.e. the SNR threshold has not been exceeded), thebuffer 120 is instructed, through control signal 118 to sample moredigital time-domain samples from the receiver at a time offset, e.g.half of a timeslot or 833 μsec of a three timeslot, 5 msec burst. Theseadditional digital time-domain samples are sampled according to asliding search window as described further with reference to FIG. 8. Asbefore, the digital time-domain samples now in the buffer 120 are sentalong first path 107 again, repeating the process of looking for one ofthe two component waveforms of the composite signal waveform, in thiscase, looking for the up-chirp waveform of the dual-chirp waveform.Further time-domain samples are processed in a like manner until theup-chirp signal is detected by the burst detection processor 116, i.e.the signal threshold has been exceeded, as described above.

In the first scenario, where the SNR threshold has been exceeded, itmust also be determined whether the “peak” of the up-chirp waveform, orthe input buffer containing the “largest portion” of the up-chirpwaveform, has been found. It is important to note that so far, thediscussion has assumed (for illustration purposes) that the peak of thedual-chirp waveform, i.e. the entire dual-chirp waveform, has beensampled at the buffer 120; however, in reality, the SNR threshold willexceeded in cases where less than the entire dual-chirp waveform hasbeen sampled at the buffer 120. For example, the 234 samples (equatingto 5 msec, which is the length of the dual-chirp waveform, of samplestaken at 46.8 kHz) from may only contain 180 samples of the dual-chirpwaveform and 54 samples of noise, which may cause the SNR threshold tobe exceeded depending on the configuration. Thus, once the SNR thresholdhas been exceeded by the computed SNR of the current digital samples atthe buffer 120, the detection and estimation processor 116 instructs thebuffer 120 (through control signal 118) to sample more digital timedomain samples from the matched filter 106.

This creates a sliding search process for the composite signal waveform,e.g. the dual-chirp waveform, on the FCCH. As such, a second inputbuffer containing samples with ½ slot delay, for example, from a firstinput buffer (which caused the SNR threshold to be exceeded) is receivedat the sample buffer 120 and processed as above in the first path 107 todetect one of the component waveforms, again, the up-chirp waveform andcompute a second SNR of the frequency representation of the desweptup-chirp waveform in the second input buffer. The second SNR is comparedwith the first SNR, as computed above. If the second SNR is greater thanthe first SNR, then a further iteration of processing (involving a thirdinput buffer offset from the second input buffer by one half of a slot)is performed and current samples are maintained for future processing,as detection is yet to occur. However, if the second SNR is not greaterthan the first SNR, then the first input buffer (that caused the SNRthreshold to be exceeded) contains the “peak” of the up-chirp waveform,or the portion of the up-chirp waveform having the highest SNR, i.e. a“peak SNR”. Each iteration process is performed in less than ½ slot, or833 μsec if the 5 msec burst occupies three timeslots. When the newinput buffer is received, a sliding window counter is incremented tochange the choice of slots to be received by a next buffer. The slidingsearch window is further described with reference to FIG. 8.

Next, following the first scenario, once the set of digital time-domainsamples containing the “peak” of the up-chirp waveform 124 from peak 140(the frequency representation of the deswept up-chirp waveform) isdetected (from the SNR that exceeds the SNR threshold the most), thenthis indicates that the largest portion of the dual-chirp waveform hasbeen received at the antenna 102 and the set of digital time-domainsamples now stored in buffer 120 are then sent along second path 109,which is analogous to the first path 107 except that the second path 109is looking for the other of the two component waveforms. In this case,the digital time-domain samples (which have previously been determinedto contain the “peak of the up-chirp waveform, and thus, the “peak ofthe down-chirp waveform) are sent in the path 109 so that the down-chirpwaveform can be deswept and isolated into a corresponding tone to bedetected also at the detection and estimation processor 116.

Thus, the detection and estimation processor sends control signal 118 tothe buffer 120 in order to begin sending the digital time-domain samplesstored in the buffer 120 along the second path 109. Again, the secondpath 109 is only taken when the peak of the up-chirp waveform has beendetected at by the burst detection processor 116 in the first path 107;thus, the peak of the down-chirp waveform will be detected now in thesecond path 109.

Following the second path 109, the time-domain digital samples at thebuffer 120 are sent to the second phase shifter 110. A frequency vs.time plot 142 is shown of the received dual-chirp waveform, showing boththe down-chirp waveform 144 and the up-chirp waveform 146. The secondphase shifter 110 desweeps the signal time-domain digital samples, i.e.r(t), with a second desweeping waveform 150, which is the complexconjugate of the component waveform that is to be detected in the secondpath 109, e.g. the down-chirp waveform of the dual-chirp waveform, butit could be the second of two component waveforms of a composite signalwaveform. In this case, the complex conjugate of the down-chirp waveformis advantageously the up-chirp waveform, which is shown as the seconddesweeping waveform 150 of the frequency vs. time plot 148 and alsorepresented mathematically as exp(+jk(t−T/2)²).

The resulting signal from the desweeping at the second phase shifter 110is shown as frequency vs. time plot 152. The deswept down-chirp waveform154, now a tone including noise (i.e. a narrow band waveform), and thephase shifted up-chirp waveform 156 are shown. Note that the frequencyof the up-chirp waveform has been shifted, i.e. doubled, which is shownas the phase shifted up-chirp waveform 156. The output of the secondphase shifter 110 is then sent to the second FFT processor 114, which issimilar to the first FFT processor 112, which translates the time-domainsignal into a frequency-domain signal including a frequencyrepresentation of the deswept down-chirp waveform 160 (or the peak 160)of frequency vs. magnitude plot 158, similar to the process performed inthe first path 107. The peak 160 is the frequency representation of thedeswept down-chirp waveform which indicates the presence of the actualdown-chirp waveform. Additionally, zero padding may be done at thesecond FFT processor 114 as needed.

Next, the output of the second FFT processor 114 is sent to thedetection and estimation processor 116; however, since the set of buffersamples containing the largest portion of the down-chirp waveform hasalready been found (since the first path has confirmed that set ofbuffer samples already contains the largest portion of the up-chirpwaveform has been found), the detection and estimation processor 116does not try to detect the down-chirp waveform and perform the SNRcomputation or the sliding search window.

Next, since both component waveforms of the composite waveform, i.e. theup-chirp and down-chirp waveforms of the dual-chirp waveform, thedetection and estimation processor 116 estimates the frequency of the ofthe frequency representation of the deswept up-chirp waveform, which isthe frequency at the peak 140 of the tone and is referred to as f_(up).This process is common in prior art acquisition systems that processtone waveforms only, and is well known in the art. One importantdistinction between such a prior art system and this embodiment of thepresent invention, however, is that the waveform sent in this embodimentis not a tone, but a composite waveform, e.g. a dual-chirp waveform,wherein the component waveforms are deswept into tones after thepossibility of incurring “spurs” into the waveform has passed. However,once deswept into tones, the detection and estimation processor 116estimates the frequency of the tone at the peak 140.

Similarly, the frequency of the frequency representation of the desweptdown-chirp waveform or peak 160 is estimated at the detection andestimation processor 116, which is referred to as f_(dn).

Furthermore, a Discrete Fourier Transform (DFT) may be performed aroundpeaks 140 and 160 (i.e. the frequency representations of the desweptup-chirp waveform and the deswept down-chirp waveform) of the output ofthe FFT to further refine the frequency estimated at the peaks 140 and160, i.e. f_(up) and f_(dn). This is further described with reference toFIG. 9.

Both of these estimates, i.e. the frequency estimate of the frequencyrepresentation of the deswept down-chirp waveform f_(dn) and thefrequency estimate of the frequency representation of the desweptup-chirp frequency f_(up), each have an unknown frequency offset and anunknown timing offset associated with them. This is represented in FIG.5D, wherein the received down-chirp waveform and the received up-chirpwaveform are both shown as having an unknown frequency offset, i.e.f_(d), and an unknown timing offset, i.e. t₀. Furthermore, arelationship exists between the frequency of deswept up-chirp waveformf_(up), f_(d), and t₀, such that:f _(up) =f _(d) −Kt ₀  (5)where K is the known sweep parameter or frequency rate-of-change of theup-chirp waveform.

Furthermore, a similar relationship exists between the frequency ofdeswept down-chirp waveform f_(dn), f_(d), and t₀, such that:f _(dn) =f _(d) +Kt ₀  (6)where K₂ is the known sweep parameter or frequency rate-of-change of thedown-chirp waveform.

Since f_(up), f_(dn), K are known, the two Equations (5) and (6) can besolved for the frequency offset f_(d), and the time offset t₀ which areneeded for the mobile terminal to synchronize with the gateway stationas in Equations (7) and (8).f _(d)=0.5(f _(up) +f _(dn))  (7)t ₀=(f _(up) −f _(dn))/2K  (8)

Thus, the frequency offset f_(d), and the time offset t₀ are estimatedand output from the detection and estimation processor 116. It isimportant to note that Equations (5) through (8) only hold true in thespecific example shown, in the case of the dual-chirp waveform.Furthermore, these equations only apply when the hypothesized waveform,i.e. the received waveform that contains the largest portion of thedual-chirp waveform, begins at t=0 sec. However, depending on the typeof composite waveform sent, the skilled artist could derive therelationships needed to solve for the frequency offset f_(d) and thetime offset t₀. Additionally, the frequency offset and timing offsetestimations are further described with reference to FIG. 9 below.

Advantageously, the matched filter 106, buffer 120, first phase shifter108, second phase shifter 110, first FFT processor, second FFTprocessor, and the detection and estimation processor 116 of theacquisition section 100 can be implemented as an application specificintegrated circuit (ASIC) or a digital signal processor.

Referring next to FIG. 8, a sliding window search process or algorithmis illustrated as may be implemented by the search algorithms employedby the detection and estimation processor 116 in the acquisition system100 of FIG. 7. Shown is the frame 200 including the burst 202 thatcontains the composite waveform, e.g. the dual-chirp waveform, slidingsearch windows 204 each offset from each other by a specified time 206.Also shown is an FFT output power vs. time plot 208 having a peak 210 atthe center of the burst 202 containing the dual-chirp waveform.

In this particular embodiment, a 5 msec burst 202 is transmitted onceevery frame 200, or 320 msec, by the gateway station of the satellitecommunications system of FIG. 1. Thus, the sliding search windows 204are 3 slots totaling 5 msec, wherein each slot is 1.67 msec in length.In between iterations, the sliding search windows 204 are moved thespecified time 206, which is shown as one half of a slot or 833 μsec. Itis noted that all of these parameters can be varied easily by theskilled artist. Note also that each sliding search window 204 has aparticular fixed overlap.

Each sliding search window 204 contains digital time-domain samplessampled at the buffer 120 of FIG. 7; thus, each sliding search window204 has “an input buffer” associated therewith. Furthermore, asillustrated, the burst 202 does not exactly correspond to the exacttiming of the sliding search windows 204; thus, there is a time offset212 (i.e. t₀) between the sliding search window (shown as sliding searchwindow 214) that contains the largest portion (or peak) of thedual-chirp waveform, as described in FIG. 7, and the actual burst 202containing the dual-chirp waveform.

Furthermore, a time τ is defined as a time at which each sliding searchwindow 204 begins. For example, τ is shown as the point in time thatsliding search window 214 begins, but is also the time that any slidingsearch window begins. The time τ is illustrated mathematically in FIG.9. Note also that every sliding search window 204 contains ahypothesized waveform, since the process is hypothesizing that thedigital samples contained within each sliding search window 204 are thecomposite waveform, when most of the time, they are not the compositewaveform.

This sliding search window diagram is related to the acquisition section100 of FIG. 7 in that sliding search windows 204 located away from thelocation of the burst, e.g. sliding search window 216, will be sampledat the buffer 120, sent through the first path 107 and the SNR thresholdwill not be exceeded (as described in FIG. 7). Thus, the buffer 120 willbe instructed to sample a new sliding search window until the SNRthreshold has been exceeded.

Furthermore, sliding search windows 218, 214, and 220 may all cause theSNR threshold to be exceeded; however, as can be seen, the input buffercontaining sliding search window 214 will contain the “peak” of thedual-chirp waveform. Thus, as described in FIG. 7, the detection andestimation processor 116 will cause the buffer 120 to sample slidingsearch windows 214 and 220, even though the SNR threshold has beenexceeded by sliding search window 218, until the input buffer (i.e. theset of samples in buffer 120 that correspond to sliding search window214) that contains the “largest portion” or peak of the burst 202 isfound, i.e. sliding search window 214.

Thus, the sliding search window process is used to scan across theentire frame 200 looking for the burst 202 containing the compositesignal waveform, in this case, the dual-chirp waveform. Once found, thedetection and estimation processor 116 of FIG. 7 then performs the abovedescribed steps to estimate a frequency offset and a timing offset ofthe burst enabling synchronization.

Referring next to FIG. 9, a flow chart is shown of an exemplary searchalgorithm employing a composite waveform, specifically the dual-chirpwaveform as illustrated in FIGS. 3 and 4 in conjunction with theacquisition section of FIG. 7 and the sliding search windows of FIG. 8.

First, digital time-domain samples (hereinafter referred to as “inputsamples”) are sampled (Step 902) for a time T in order to search for thecomposite waveform, e.g. the dual-chirp waveform. This step is typicallyperformed by an input buffer (e.g. buffer 120) at an acquisition section(e.g. acquisition section 100) of a mobile terminal. Time T is typicallya length of time corresponding to the length of the burst that containsthe dual-chirp waveform, e.g. T is 5 msec.

The input samples are first processed by desweeping a possible up-chirpwaveform and performing a Fast Fourier Transform (FFT) thereon (Step904), as described earlier herein in FIG. 7. The desweeping of thepossible up-chirp waveform may be done at the first phase shifter 108 ofFIG. 7 by multiplying a first desweeping waveform 130 d(t), which is thecomplex conjugate of the up-chirp waveform or the down-chirp waveform.The FFT may be performed at the first FFT processor 112 of FIG. 7.

Next, the signal-to-noise ratio (SNR) is computed for the frequencyrepresentation of the deswept up-chirp waveform, such as described inFIG. 7 at the detection and estimation processor 116, and compared tothe SNR threshold (Step 906), as described again with reference to FIG.7.

If the computed SNR does not exceed the SNR threshold (Step 906), thensoftware in the detection and estimation processor 116 increments thescanning parameter by a specified time offset 206 (Step 908), shown inFIG. 8, for example, corresponding to scanning time with reference to acontinuous time t. This effectively moves the sliding search window overby the specified time offset 206, e.g. 833 μsec.

If the computed SNR exceeds the SNR threshold (Step 906), then an actualup-chirp waveform is detected (as a frequency representation 140 of thedeswept up-chirp waveform, i.e. peak 140 of FIG. 7), and a discreteFourier transform (DFT) is performed (Step 910) on the input samples(within the sliding search window) by the detection and estimationprocessor 116, as described in briefly earlier and in more detail below.

With respect to performing a DFT, in one embodiment, fine frequencyestimation using a DFT as previously described is performed as part offrequency interpolation in the detection and estimation processor 116.When the up-chirp waveform is detected as described above, a DFT isestimated around a coarse detected frequency in increments of ±20 Hz torefine the frequency estimation of the frequency representation of thedeswept up-chirp waveform; thus, the measurement of f_(up) in Equation(5) is refined.

As such, the DFT is represented as the equation describing a magnitudeY(m) for a group d for N samples is:

$\begin{matrix}{{Y(m)} = {\sum\limits_{n = 0}^{N - 1}\;{{x(n)}{\mathbb{e}}^{{{- {j2}}\;\pi\; n\;{m/N}}\;}}}} & (9)\end{matrix}$where X(n) is the deswept up-chirp waveform.

A peak value of a group of Y(m) values is selected at a peak frequencyF_(peak). If a corresponding Y(m) is denoted as p₂, then frequencies oneach upper and lower side of p₂, i.e. frequencies at p₁ and p₃, are usedto perform interpolation.

In one embodiment interpolation is performed using a quadratic fit; inanother embodiment interpolation is performed using a sincinterpolation, which uses an infinite series to treat all such Y(m)samples as perfect samples.

For a quadratic fit, Equations (10) and (11) are used to determineestimated frequency F_(est):F _(adj)=0.5*(p ₁ −p ₃)/(p ₁ +p ₃−2p ₂)  (10)F _(est) =F _(peak)+(F _(adj)*20.0)  (11)

Other methods for interpolation are also possible in keeping with thespirit of the present invention.

After the DFT is performed on the frequency representation of theup-chirp waveform (Step 910), the input samples, stored in the buffer120, which correspond to the down-chirp component waveform, are desweptand an FFT and DFT are performed (Step 912), respectively. For example,this may be done in the second path 109 of FIG. 7.

Finally, the frequency offset f_(d) and the timing offset t₀ of thedual-chirp waveform are estimated (Step 914) by a parameter estimator(not shown) of the detection and estimation processor 116, as describedwith reference to FIG. 7. The results of Steps 910 and 912 produce twofrequency estimates, one for the frequency representation of the desweptup-chirp waveform and one for the frequency representation of thedeswept down-chirp waveform. As described earlier, each frequencyestimation, e.g. f_(up) and f_(dn), has an unknown frequency offset,i.e. f_(d), and an unknown timing offset, i.e. t₀. Furthermore, arelationship exists between f_(up), and f_(d) and to of the receiveddual-chirp waveform, in Equation (5) above, and a similar relationshipexists between f_(dn), and f_(d) and t₀ of the received dual-chirpwaveform, in Equation (6) above. Thus, as described above, theserelationships are both used to solve for the frequency offset f_(d), andthe time offset t₀ (Step 914) as can be done in Equations (7) and (8),which are required for the mobile terminal to synchronize with thegateway station. The step is simplified in the dual-chirp waveform,since both the up-chirp waveform and the down-chirp waveform have afrequency that varies linearly with time and each is the complexconjugate of the other. Thus, the up-chirp waveform and the down-chirpwaveform is easily expressible in mathematical terms and equations.

Next, the following detailed mathematical analysis is presented toillustrate, mathematically, the search algorithms used in theacquisition process of FIG. 9, performed by the acquisition section ofFIG. 7.

In accordance with the invention herewith, the search algorithmsemployed by the Acquisition System 100 accomplishes detection of theactual up-chirp waveform and the actual down-chirp wave form, as well asthe frequency and time estimation, by designing a complex basebanddual-chirp signal burst as shown in FIG. 3 and representedmathematically in Equation 12.

$\begin{matrix}{{s(t)} = {{2{{p(t)} \cdot {\cos\left\lbrack {\pi\;{K\left( {t - \frac{T}{2}} \right)}^{2}} \right\rbrack}}} = {{s_{1}(t)} + {s_{2}(t)}}}} & (12)\end{matrix}$where

$\begin{matrix}{{p(t)}\left\{ \begin{matrix}{1,} & {0 \leq t \leq T} \\{0,} & {else}\end{matrix} \right.} & (13)\end{matrix}$and wherein

$\begin{matrix}{{s_{1}(t)} = {{{p(t)} \cdot \exp}\left\{ {j\;\pi\;{K\left( {t - \frac{T}{2\;}} \right)}^{2}} \right\}}} & (14)\end{matrix}$and

$\begin{matrix}{{s_{2}(t)} = {{{p(t)} \cdot \exp}\left\{ {{- j}\;\pi\;{K\left( {t - \frac{T}{2}} \right)}^{2}} \right\}}} & (15)\end{matrix}$

In equation 10, s(t) denotes the dual-chirp waveform, transmitted as aburst to the mobile terminal before attenuation, time delays, andfrequency offsets are applied during transmission of the of thedual-chirp waveform over the communications links between the gatewaystation and the mobile terminal. Thus, s(t) is the source signal beingtransmitted from the transmitter 32 in FIG. 2.

In the above equations 10 through 13, T denotes a period of the burst(e.g. 5 msec) and t denotes instantaneous time measured from thestarting time of the burst in time domain. The up-chirp waveform isrepresented by s₁(t), and the down-chirp waveform is represented bys₂(t). Furthermore, p(t) is a window defining an envelope of the signalin time or a ramping function as described above at Equation (2). K isthe sweep rate parameter or the frequency rate-of-change for both theup-chirp waveform and the down-chirp waveform as described in Equations(3) and (4) above. Note that advantageously, K is the same for both theup-chirp waveform and the down-chirp waveform, except that they are theopposite direction (+K and −K); however, the skilled artist could varythis relationship while at the same time vary the above equations.

A phase, φ(t), of the dual-chirp signal of duration T is equal toEquation (16).

$\begin{matrix}{{\varphi(t)} = {\pi\;{K\left( {t - \frac{T}{2}} \right)}^{2}}} & (16)\end{matrix}$

Within the burst containing the dual chirp signal, an instantaneousfrequency for the up-chirp waveform, s₁(t) equals K(t−T/2), wherein K isa frequency rate-of-change, and an instantaneous frequency for thedown-chirp waveform s₂(t) equals −K(t−T/2); therefore, instantaneousfrequencies for s₁(t) and s₂(t) vary from −KT/₂ to KT/₂. The frequencyspan or frequency bandwidth of the dual-chirp signal is therefore β=KT.

Next, at the receiver 44 (i.e. the mobile terminal), the received burstcontaining a received dual-chirp waveform (i.e. one example of areceived composite waveform), r(t) is corrupted by frequency shifting(+e^(j2πf) ^(d) ^(t)) due primarily to Doppler, a time delay t₀, and byAdditive White Guassian Noise (AWGN) n(t). These contributing factorsare described above with reference to FIG. 2. Therefore, the receiveddual-chirp waveform is represented as Equation 17.r(t)=A·s(t−t ₀)exp{2πf _(d) t+φ}+n(t)=A·[s ₁(t−t ₀)+s ₂(t−t ₀)] exp{2πf_(s) t+φ}+n(t)  (17)wherein A is an amplitude of the received waveform r(t), wherein t₀ isthe time delay or propagation delay, wherein f_(d) is a frequency offsetbetween the transmitter 32 and the receiver 44, which is due to Dopplerfrequency shifting, wherein φ is a random phase in [0,2π], and whereinn(t) is additive white Guassian noise (AGWN) having zero mean andspectral density N₀.

As such, the acquisition system 100 described in FIG. 7 of the mobileterminal receives this waveform. Using the mathematical representationr(t) described by Equation (17), it is possible for the acquisitionsystem 100 to multiply r(t) with a proper desweeping waveform d(t) suchthat v(t)=r(t)d(t). Consistent with that described in FIG. 7, thedesweeping waveform d(t) would be the complex conjugate of the waveformbeing searched for. In the case of the dual-chirp waveform, d(t) is thefirst desweeping waveform 130, which is the complex conjugate of theup-chirp waveform which is the down-chirp waveform. Such complexconjugate of the waveform begin searched for is represented at time t−τ,wherein τ is the point in time that the hypothesized composite waveformwill start, as illustrated in FIG. 8.

A deswept up-chirp waveform is represented by v₁(t) Equation (18) intime domain. Note that the deswept up-chirp waveform 134 is shown in thefrequency domain in frequency vs. time plot 132 of FIG. 7. A desweptdown-chirp waveform is represented as v₂(t) by Equation (19) in timedomain. Similarly, the deswept down-chirp waveform 154 is shown in thefrequency domain in plot 152 of FIG. 7. Furthermore, this assumes anactual up-chirp waveform or down-chirp waveform is present in r(t).v ₁(t)=r(t)·s ₁*(t−τ)=v ₁₁(t)+v ₂₁(t)+N ₁(t)  (18)v ₂(t)=r(t)·s ₂*(t−τ)=v ₁₂(t)+v ₂₂(t)+N ₂(t)  (19)wherein

$\begin{matrix}\begin{matrix}{{v_{11}(t)} = {{{As}_{1}\left( {t - t_{0}} \right)}{s_{1}^{*}\left( {t - \tau} \right)}\exp\left\{ {{2\pi\; f_{d}t} + \phi} \right\}}} \\{= {A\;\exp\;\left\{ {j\left\lbrack {{\pi\;{K\left( {t_{0} - \tau} \right)}\left( {t_{0} + \tau + T} \right)} +} \right.} \right.}} \\{\left. \left. \phi \right\rbrack \right\}\exp{\left\{ {{j2\pi}\;{K\left\lbrack {\left( {\tau - t_{0}} \right) + \frac{f_{d}}{K}} \right\rbrack}t} \right\} \cdot {p\left( {t - t_{0}} \right)}}{p\left( {t - \tau} \right)}}\end{matrix} & (20)\end{matrix}$

$\quad\begin{matrix}\begin{matrix}{{v_{21}(t)} = {{{As}_{2}\left( {t - t_{0}} \right)}{s_{2}^{*}\left( {t - \tau} \right)}\exp\left\{ {{2\;\pi\; f_{d}t} + \phi} \right\}}} \\{= {A\;\exp\left\{ {{{- {j\pi}}\frac{K}{2}\left( {\tau - t_{0}} \right)^{2}} +} \right.}} \\{\left. {j\;\phi} \right\}\exp{\left\{ {{{- {j2}}\;\pi\;{K\left( {t - {\frac{1}{2}\left( {t_{0} + \tau + T} \right)}} \right)}^{2}} + {{j2}\;\pi\; f_{d}t}} \right\} \cdot}} \\{{p\left( {t - t_{0}} \right)}{p\left( {t - \tau} \right)}}\end{matrix} & (21)\end{matrix}$

$\quad\begin{matrix}\begin{matrix}{{v_{12}(t)} = {{{As}_{1}\left( {t - t_{0}} \right)}{s_{2}^{*}\left( {t - \tau} \right)}\exp\left\{ {{2\;\pi\; f_{d}t} + \phi} \right\}}} \\{= {A\;\exp\left\{ {{j\;\pi\frac{K}{2}\left( {\tau - t_{0}} \right)^{2}} +} \right.}} \\{\left. {j\;\phi} \right\}\exp{\left\{ {{{- {j2}}\;\pi\;{K\left( {t - {\frac{1}{2}\left( {t_{0} + \tau + T} \right)}} \right)}^{2}} + {{j2}\;\pi\; f_{d}t}} \right\} \cdot}} \\{{p\left( {t - t_{0}} \right)}{p\left( {t - \tau} \right)}}\end{matrix} & (22)\end{matrix}$

$\quad\begin{matrix}\begin{matrix}{{v_{22}(t)} = {{{As}_{2}\left( {t - t_{0}} \right)}{s_{2}^{*}\left( {t - \tau} \right)}\exp\left\{ {{2\;\pi\; f_{d}t} + \phi} \right\}}} \\{= {A\;\exp\left\{ {j\;\left\lbrack {{\pi\;{K\left( {\tau - t_{0}} \right)}\left( {t_{0} + \tau + T} \right)} +} \right.} \right.}} \\{\left. \left. \phi \right\rbrack \right\}\exp{\left\{ {{j2}\;\pi\;{K\left\lbrack {\left( {t_{0} - \tau} \right) + \frac{f_{d}}{K}} \right\rbrack}t} \right\} \cdot {p\left( {t - t_{0}} \right)}}{p\left( {t - \tau} \right)}}\end{matrix} & (23)\end{matrix}$and whereinN ₁(t)=n(t)s ₁*(t−τ)  (24)N ₂(t)=n(t)s ₂*(t−τ)  (25)

In the above Equations, s*₁(t−τ) is the complex conjugate of s₁(t−τ) ord₁(t−τ), for example, s*₁(t) is shown as the first desweeping waveform130 (s*₁(t)=d₁(t)) in FIG. 7. Similarly, s*₂(t−τ) is the complexconjugate of s₂(t−τ) or d₂(t−τ), for example, s*₂(t) is shown as thesecond desweeping waveform 150 in FIG. 7.

Furthermore v₁₁(t) and v₂₂(t), are shown as continuous wave signals. Forexample, in a frequency vs. time plot, v₁₁(t) is shown as desweptup-chirp waveform 134 (which is tone-like or narrowband) of FIG. 7 andv₂₂(t) is shown as deswept down-chirp waveform 154 (which is tone-like)in FIG. 7. Cross-talk terms v₂₁(t) and v₁₂(t) remain as widebandchirp-like signals. For example, in a frequency vs. time plot, v₂₁(t) isshown as phase shifted down-chirp 136 in FIG. 7 and v₁₂(t) is shown asphase shifted up-chirp 156 of FIG. 7. It can be proven that thesecross-talk terms v₂₁(t) and v₁₂(t) carry much less power than thedesired continuous wave signal (tone or sinusoid) if KT²=βT is largeenough.

Therefore, if the frequency span or the frequency bandwidth β of theup-chirp waveform defined earlier herein as KT, is large enough, suchthat KT² is comparatively large enough to be neglected in themathematical analysis then frequency shift and time delay informationcan be extracted from the peak frequency.

An example of a bandwidth β large enough to reflect the cross-talk termswould be a β rendering the cross-talk terms (chirp-like signals) aboutan order of magnitude smaller than the continuous wave signals (terms).Another example of a bandwidth β large enough for reflecting resultingcross-terms would be a β which is about 80% of a bandwidth of an FCCHchannel, for example, since an FCCH channel must have sufficientbandwidth to operate in a practical manner in a wireless communicationsystem.

A skilled artisan will observe many other ways to set an appropriatebandwidth β for the up-chirp and down-chirp waveform in accordanceherewith.

Preferably, a bandwidth of a dual-chirp waveform and a differencebandwidth between the bandwidth of the up-chirp and the down-chirpwaveform should be in an order of the available bandwidth of the FCCHchannel. Minimally, the bandwidth β should be greater than 10% of theavailable bandwidth of the channel.

Next, a frequency domain representation (e.g. peak 140), V₁₁(f), of thetime domain deswept up-chirp waveform v₁(t) and a frequency domainrepresentation (e.g. peak 160), V₂₂(f) of the time domain desweptdown-chirp waveform V₂(t) are illustrated by Equations (26) and (27).The FFT is performed in Step 904 and Step 912 for the deswept up-chirpwaveform and the deswept down-chirp waveform, respectively.V ₁(f)=V ₁₁(f)+N ₁(f)  (26)V ₂(f)=V ₂₂(f)+N ₂(f)  (27)wherein V₁(f) is shown in plot 138 of FIG. 7 and V₂(f) is shown in plot158 of FIG. 7, and wherein

$\begin{matrix}\begin{matrix}{{{{{V_{11}(f)}} = {A\frac{\sin\left\lbrack {{\pi\left( {f_{d} - f + {K\left( {\tau - t_{0}} \right)}} \right)}\left( {T - {{\tau - t_{0}}}} \right)} \right\rbrack}{\pi\left( {f_{d} - f + {K\left( {\tau - t_{0}} \right)}} \right)}}},{{t_{0} - T} \leq \tau}}{\leq {t_{0} + T}}} \\{= {{A\left( {T - {{\tau - t_{0}}}} \right)}\sin\; c\left\{ {\left( {f_{d} - f + {K\left( {\tau - t_{0}} \right)}} \right)\left( {T - {{\tau - t_{0}}}} \right)} \right\}}}\end{matrix} & (28) \\\begin{matrix}{{{{{V_{22}(f)}} = {A\frac{\sin\left\lbrack {{\pi\left( {f_{d} - f - {K\left( {\tau - t_{0}} \right)}} \right)}\left( {T - {{\tau - t_{0}}}} \right)} \right\rbrack}{\pi\left( {f_{d} - f + {K\left( {\tau - t_{0}} \right)}} \right)}}},{{t_{0} - T} \leq \tau}}{\leq {t_{0} + T}}} \\{= {{A\left( {T - {{\tau - t_{0}}}} \right)}\sin\; c\left\{ {\left( {f_{d} - f - {K\left( {\tau - t_{0}} \right)}} \right)\left( {T - {{\tau - t_{0}}}} \right)} \right\}}}\end{matrix} & (29)\end{matrix}$

Determining an estimated frequency for the frequency representation ofthe deswept up-chirp waveform v₁(t) and the frequency representation ofthe deswept down-chirp waveform v₂(t), designated respectively as f_(m)and {tilde over (f)}_(m), is done by finding a frequency correspondingto a largest amplitude of the fast Fourier transform in an up-chirp anddown-chirp path. The deswept up-chirp frequency f_(m) (also referred toas f_(up) in Equation (5)) is given by Equation (30) and the desweptdown-chirp frequency {tilde over (f)}_(m) (also referred to as f_(dn) inEquation (6)), is given by Equation (31), theoretically.

In practice, the frequency estimates f_(m) and {tilde over (f)}_(m) alsocalled peak frequency estimates, are subject to noise disturbance.Nevertheless, they are unbiased estimates of true frequencies of theup-chirp waveform and the down-chirp waveform contained in the receivedwaveform, r(t).

Advantageously, knowing the two frequency estimates f_(m) and {tildeover (f)}_(m) (also referred to as f_(up) and f_(dn)), and therelationships expressed by Equations (30) and (31), an estimate ofDoppler frequency shift (or error frequency) {circumflex over (f)}_(d)and a time delay estimate {circumflex over (t)}₀ may be obtained(Equations (32) and (33)) as follows:f _(m) =f _(d) +K(τ−t ₀)  (30){tilde over (f)}_(m) =f _(d) −K(τ−t ₀)  (31){circumflex over (f)} _(d)+0.5({circumflex over (f)}_(m) {tilde over({circumflex over (f)} _(m))  (32)

$\begin{matrix}{{\hat{t}}_{0} = {\tau - \frac{\left( {{\hat{f}}_{m} - {\hat{\overset{\sim}{f}}}_{m}} \right)}{2K}}} & (33)\end{matrix}$where τ is the start time of the hypothesized composite waveform or thetime from t=0 that the set of buffer samples that contains the largestportion of the dual-chirp waveform. Time τ is further described in FIG.8. Note that in Equations (5) through (8), τ=0.

Again, as stated earlier, the relationships illustrated in Equations(30) and (31) provide, mathematically, two different equations havingtwo unknowns, which are solved for. The dual-chirp waveform, asdescribed above is an example of a composite waveform that is expressedin terms of Equations (30) and (31). Alternatively, other types ofcomposite waveforms may be used; however, depending on the specificcharacteristics of the component waveforms of the composite waveform,modeling such component waveforms into relationships between thefrequency and timing offsets, as shown in Equations (30) and (31), maybe more difficult, for example, if the component waveforms do not havefrequencies that vary linearly with time. Thus, the mathematicalanalysis will have to be adjusted.

As for the case of a composite waveform as shown in FIGS. 6A through 6D,the two equations, e.g. Equations (30) and (31), for this compositewaveform would essentially provide the same relationship for each of thecomponent waveforms. The result would be two equations each having twounknowns (i.e. f_(d) and t₀); however, both equations would essentiallybe the same, yielding inconclusive estimates of the frequency and timingoffsets. In contrast, as shown above, a composite waveform meeting thethree design characteristics described above, such as the dual-chirpwaveform, will yield accurate measurements of the frequency and timingoffsets needed for synchronization while avoiding the problems of theprior art acquisition schemes, e.g. mitigates unmodulated spurs, can beused with an FFT, no modifications to the receiver hardware, efficientuse of processing bandwidth, and supports acquisition of voice andtracking of alerting services in the same composite waveform.

Finally, referring next to FIG. 10, a plot 1002 of the amplitude of aFourier Transform Peak versus time (i.e. searching time) is shown. Anestimate of the Burst's time of arrival can be obtained by determiningthe peak of a triangle shown in FIG. 10. Thus, at the peak of the plot,the composite signal waveform, e.g. the dual-chirp waveform, hascompletely arrived (the largest portion of the dual-chirp waveform ispresent in the input buffer) at the acquisition section of the mobileterminal.

While the invention herein disclosed has been described by means ofspecific embodiments and applications thereof, numerous modificationsand variations could be made thereto by those skilled in the art withoutdeparting from the scope of the invention set forth in the claims.

1. A method for enabling synchronization of a communications terminal ina wireless communication system comprising: receiving a burst at areceiver of the communications terminal, the burst containing acomposite waveform including two or more component waveforms, whereineach of the two or more waveforms has a known frequency variationthroughout the burst; estimating a frequency offset and a timing offsetof said composite waveform as received into said receiver whereby saidsynchronization of said communications terminal is achieved; detecting afirst component waveform of said two or more component waveforms, anddetecting a second component waveform of said two or more waveforms,wherein said detecting said first component waveform comprisesdesweeping said first component waveform into a first deswept componentwaveform, wherein said first deswept component waveform is a narrow bandwaveform; transforming said first deswept component waveform into afirst frequency domain representation; estimating a signal-to-noiseratio of said first frequency domain representation; comparing saidsignal-to-noise ratio of said first frequency domain representation to athreshold; estimating, in the event said threshold is exceeded, a firstpeak frequency of said first frequency domain representation; desweepingsaid second component waveform of said two or more component waveformsinto a second deswept component waveform; transforming said seconddeswept component waveform into a second frequency domainrepresentation; and estimating a second peak frequency from said secondfrequency domain representation; and wherein said estimating comprisesestimating, using said first peak frequency and said second peakfrequency and said known frequency variation of each of said firstcomponent waveform and said second component waveform; and wherein saidfrequency offset is defined by the formula:f _(d)=0.5(f ₁ +f ₂) wherein f_(d) is said frequency offset in Hertz, f₁is said first peak frequency in Hertz, and f₂ is said second peakfrequency in Hertz.
 2. A method for enabling synchronization of acommunications terminal in a wireless communication system comprising:receiving a burst at a receiver of the communications terminal, theburst containing a composite waveform including two or more componentwaveforms, wherein each of the two or more waveforms has a knownfrequency variation throughout the burst; estimating a frequency offsetand a timing offset of said composite waveform as received into saidreceiver whereby said synchronization of said communications terminal isachieved; detecting a first component waveform of said two or morecomponent waveforms, and detecting a second component waveform of saidtwo or more waveforms, wherein said detecting said first componentwaveform comprises desweeping said first component waveform into a firstdeswept component waveform, wherein said first deswept componentwaveform is a narrow band waveform; transforming said first desweptcomponent waveform into a first frequency domain representation;estimating a signal-to-noise ratio of said first frequency domainrepresentation; comparing said signal-to-noise ratio of said firstfrequency domain representation to a threshold; estimating, in the eventsaid threshold is exceeded a first peak frequency of said firstfrequency domain representation; desweeping said second componentwaveform of said two or more component waveforms into a second desweptcomponent waveform; transforming said second deswept component waveforminto a second frequency domain representation; and estimating a secondpeak frequency from said second frequency domain representation; andwherein said estimating comprises estimating, using said first peakfrequency and said second peak frequency and said known frequencyvariation of each of said first component waveform and said secondcomponent waveform; and the method of claim 1 wherein said timing offsetis defined by the formula:t ₀=τ−[(f ₁ −f ₂)/2K] wherein f₁ is said first peak frequency in Hertz,f₂ is said second peak frequency in Hertz, K is the absolute value ofsaid known frequency variation of said each of said first componentwaveform and said second component waveform in Hertz/second, and τ is atime in seconds at which said composite waveform is hypothesized toarrive at said communications terminal.
 3. An acquisition system of awireless communications terminal for acquiring a received compositewaveform including two or more component waveforms and estimating afrequency offset and a timing offset of the received composite waveformcomprising: a first phase shifter for desweeping a first componentwaveform of the received composite waveform; and a first processorcoupled to the first phase shifter for transforming the first componentwaveform having been deswept into a first frequency domainrepresentation.
 4. The system of claim 3 wherein said first processor isa first fast Fourier transform processor.
 5. The system of claim 3further comprising a detection processor coupled to said first processorfor detecting a peak of said first frequency domain representation,whereby detecting the presence of said first component waveform.
 6. Thesystem of claim 5 wherein said detection processor estimates a firstpeak frequency of said first frequency domain representation.
 7. Thesystem of claim 6 wherein said detection processor includes a discreteFourier transform for fine-tuning the estimation of said first peakfrequency.
 8. The system of claim 5 further comprising: a second phaseshifter for desweeping a second component waveform of said receivedcomposite waveform; and a second processor coupled to the second phaseshifter for transforming the second component waveform, having beendeswept, into a second frequency domain representation.
 9. The system ofclaim 8 wherein said second processor is a second fast Fourier transformprocessor.
 10. The system of claim 8 further comprising a detectionprocessor coupled to said second processor for detecting a peak of saidsecond frequency domain representation.
 11. The system of claim 10wherein said detection processor estimates a second peak frequency ofsaid second frequency domain waveform.
 12. The system of claim 11wherein said detection processor includes a discrete Fourier transformfor fine-tuning the estimation of said second peak frequency.
 13. Thesystem of claim 11 wherein said detection processor includes a parameterestimator for computing said frequency offset and said timing offset ofsaid received composite waveform.
 14. The system of claim 3 wherein saidreceived composite waveform comprises a received dual-chirp waveform.15. The system of claim 3 further comprising: a matched filter forfiltering the received composite waveform; and a buffer coupled to thematched filter, wherein the buffer is further coupled to said firstphase shifter.